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arXiv · 2207.05504

Quantum loop groups for symmetric Cartan matrices

Andrei Neguţ
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Abstract

We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators $\{e_{i,k}, f_{i,k}\}_{i \in I, k \in \mathbb{Z}}$ in order for the natural Hopf pairing between the positive and negative halves of the quantum loop group to be perfect. As an application, we describe the localized K-theoretic Hall algebra of any quiver without loops, endowed with a particularly important $\mathbb{C}^*$ action.

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BibTeXRIS

Andrei Neguţ. 2022-07-12. Quantum loop groups for symmetric Cartan matrices. https://arxiv.org/abs/2207.05504

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